# The Fine Picture

# The Fine Picture

This chapter restricts the *m*-tuple (*f _{i}*) of demand functions defining the exchange model to belong to ε

_{c}. In addition to the assumptions made in the previous chapters (recall that ε

_{c}is a subset of ε

_{r}), the demand function

*f*satisfies the weak axiom of revealed preferences for every consumer, and the slightly stronger negative definiteness of the Slutsky matrix for the consumer whose demand function satisfies desirability (A). These stronger assumptions are aimed at giving more economic flesh to the exchange model. As a consequence, the natural projection inherits much stronger properties that give a specificity of its own to the exchange model. The most important properties of the exchange model with (

_{i}*f*) ɛ ε

_{i}_{c}are the regularity of the no-trade equilibria, the openness and full measure (a.k.a., the genericity) of the set of regular equilibria as a subset of the equilibrium manifold, the inclusion of the set of equilibrium allocations in one and only one connected component of the set of regular economies, the uniqueness of equilibrium for all economies belonging to that component, and the interpretation of that property in terms of trade intensity.

*Keywords:*
general equilibrium model, demand functions, no-trade equilibrium, no-trade equilibria, natural projection, exchange model

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